Multivariable Calculus

Lecturer: Professor Denis Auroux
College/University: Massachusetts Institute of Technology (MIT)

1. Dot Product
   
2. Determinants and Cross Product.
   
3. Matrices and Inverse Matrices
   
4. Square Systems; Equations of Planes
   
5. Parametric Equations for Lines and Curves
   
6. Velocity, Acceleration; Kepler's Second Law
   
7. Review
   
8. Level Curves; Partial Derivatives; Tangent Plane Approximation
   
9. Max-min Problems; Least Squares
   
10. Second Derivative Test; Boundaries and Infinity
    
11. Differentials; Chain Rule
    
12. Gradient; Directional Derivative; Tangent Plane
    
13. Lagrange Multipliers
    
14. Non-independent Variables
    
15. Partial Differential Equations
    
16. Double integrals
    
17. Double integrals in Polar Coordinates; Applications
    
18. Change of Variables
    
19. Vector Fields and Line Integrals in the Plane
    
20. Path Independence and Conservative Fields.
    
21. Gradient Fields and Potential Functions
    
22. Green's Theorem
    
23. Flux; Normal Form of Green's Theorem
    
24. Simply Connected Regions
    
25. Triple Integrals in Rectangular and Cylindrical Coordinates
    
26. Spherical Coordinates; Surface Area
    
27. Vector Fields in 3D; Surface Integrals and Flux
    
28. Divergence Theorem (First Part)
    
29. Divergence theorem (Second Part)
    
30. Line Integrals in Space, Curl, Exactness and Potentials
    
31. Stokes' Theorem (First Part)
    
32. Stokes' theorem (Second Part)
    
33. Topological considerations; Maxwell's equations
    
34. Review (First Part)
    
35. Review (Second Part)